On a non-self adjoint expansion formula

Abstract

This paper develops a formula of inversion for an integral transform of the kind similar to that associated with the names of Kontorovich and Lebedev except that the kernel involves the Neumann function Yu(kr) and the variable r varies over the infinite interval a≤r0 The transform is useful in the investigation of functions that satisfy the Helmholtz equation and a condition of radiation at infinity. The formula established is expressed entirely in terms of series expansions and replaces earlier inversion formulas that require the evaluation of contour integrals.

Keywords

• integral transforms
• eigenfunction expansions
• Bessel functions.